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- W3212502012 abstract "We prove the boundedness of the non-local operator [ mathcal{L}^a u(x)=int_{mathbb{R}^d} left(u(x+y)-u(x)-chi_alpha(y)big(nabla u(x),ybig)right) a(x,y)frac{dy}{|y|^{d+alpha}} ] from $H_{p,w}^alpha(mathbb{R}^d)$ to $L_{p,w}(mathbb{R}^d)$ for the whole range of $p in (1,infty)$, where $w$ is a Muckenhoupt weight. The coefficient $a(x,y)$ is bounded, merely measurable in $y$, and H{o}lder continuous in $x$ with an arbitrarily small exponent. We extend the previous results by removing the largeness assumption on $p$ as well as considering weighted spaces with Muckenhoupt weights. Using the boundedness result, we prove the unique solvability in $L_p$ spaces of the corresponding parabolic and elliptic non-local equations." @default.
- W3212502012 created "2021-11-22" @default.
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- W3212502012 date "2021-11-07" @default.
- W3212502012 modified "2023-09-23" @default.
- W3212502012 title "Boundedness of non-local operators with spatially dependent coefficients and $L_p$-estimates for non-local equations" @default.
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- W3212502012 doi "https://doi.org/10.48550/arxiv.2111.04029" @default.
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